Discussion of An empirical analysis of the pricing of collateralized Debt obligation by Francis Longstaff and Arvind Rajan
|
|
- Carmel Moore
- 5 years ago
- Views:
Transcription
1 Discussion of An empirical analysis of the pricing of collateralized Debt obligation by Francis Longstaff and Arvind Rajan Pierre Collin-Dufresne GSAM and UC Berkeley NBER - July 2006
2 Summary The CDS/CDX Market The CDO Market New modeling approach Empirical implementation Conclusion
3 Summary of the paper This paper studies an interesting new data set on a new market: Synthetic CDO tranches It develops an elegant reduced form model in the spirit of Duffie & Garleanu It empirically fits the model to the data by minimizing sum of squared errors and finds: Three factors are needed to fit tranche spreads on five tranches. These are three stochastic intensity processes that govern the default arrival of respectively: Single firm default (1 firm defaults on average every 1.2 years) Joint industry wide defaults (15 firms default jointly on average every 42.5 years) Economy wide defaults (88 firms default jointly on average every 763 years) The model fit is very good. The RMSE is around 3 to 5 bps. Paper concludes that Pricing in these markets is highly efficient. This is true even during the credit crisis of May 2005 which resulted in major losses for a number of major credit-oriented hedge funds.
4 Rapid evolution of credit markets Innovation in contracts, from traditional funded securities: corporate bonds to new unfunded derivatives: credit default swaps (CDS) And increased liquidity, Allow investors to express views on: Single-names CDS Baskets of names (CDX.IG, CDX.HV, itraxx) Correlation (Synthetic liquid CDO, Bespoke CDO, CDO 2... ) Emerging Market Countries (EMCDS) Basket of Countries (EMCDX)
5 CDS Contract Structure A CDS is an insurance contract against a credit event of counterparty: Prior to credit event: protection buyer notional spread protection seller Upon arrival of credit event: protection buyer protection buyer deliverable bond notional protection seller protection seller Definition of credit event: Bankruptcy Failure to pay Obligation acceleration or default Repudiation/moratorium Restructuring (Full R, Mod R, ModMod R, No R)
6 Arbitrage Relation Buy XYZ bond + Buy XYZ protection Earn risk-free rate Buy risk-free bond + Sell XYZ protection Earn XYZ bond yield CDS spread Y XYZ R f CDS allows pure unfunded play on credit risk. Empirical evidence on Basis = CDS spread (Y XYZ R f ). Basis wrt Tsy (bp) Basis wrt Swap (bp) implied R f / Tsy Mean S.E. (of mean) Mean S.E. Mean S.E. Aaa/Aa A Baa All Categories source: Hull, Pedrescu, White (2006)
7 The CDX index The CDX index is an insurance contract against credit events of a portfolio of counterparties (e.g., 125 names in CDX.IG): Prior to credit event: protection buyer outstanding notional spread protection seller Upon arrival of credit event of XYZ: protection buyer protection buyer XYZ delivervable bond XYZ notional protection seller protection seller Following credit event outstanding notional is reduced by notional of XYZ in portfolio 1 (i.e., in CDX.IG). 125 Contract expires at maturity or when notional exhausted. N.B.: CDX contract equally weighted portfolio of single name CDS contracts CDX spread average of single name CDS spreads
8 Market Overview Growth Rate (notional) Industry Composition of CDX.IG CDX.IG Moody s Ratings End Users source: BBA & White (2006)
9 Synthetic CDO Tranches Selling protection on CDO tranche with attachment points [L, U] (i.e., notional = U L) written on underlying basket of 125 single names (CDX): Prior to a credit event: protection buyer outstanding notional spread protection seller Upon arrival of credit event (LGD = notional P deliverable bond price), if cumulative 125 loss exceeds lower attachment point (i.e., L t = i=1 LGD i 1 {τi > L) then t} protection buyer min(lgd,outstanding notional) protection seller Following credit event outstanding tranche notional is reduced by LGD (up to exhaustion of outstanding notional). Contract expires at maturity or when tranche notional is exhausted. Tranche payoff is call spread on cumulative loss: max(l t L, 0) max(l t U, 0). Tranche valuation depends on entire distribution of cumulative portfolio losses and crucially on default event correlation model.
10 Market Size Liquid tranche market is growing steadily Bespoke portfolio credit swap market is roughly ten times the size of the index tranche market.
11 Market Model: Implied Gaussian Copula Correlation Market standard for quoting CDO tranche prices is the implied correlation of the Gaussian Copula framework. Intuition builds on structural model of default (CDO model due to Vasicek 1987): Each name in basket characterized by an asset value driven by two factors: a common market factor and an idiosyncratic factor (V i = ρ i M + 1 ρ i ɛ i with M, ɛ i independent centered Gaussian). Pairwise asset correlation is the product of the individual asset betas ( ρ i ρ j ). Default occurs when asset value falls below a constant barrier (DefProb = P(V i B i )). Market convention for quoting tranche values in terms of implied correlation assumes: The individual beta is identical across all names in the basket. The default boundary is identical and calibrated to average CDS level (or index level) All firms have identical LGD of 60%. With these heroic assumptions, a single number, the implied correlation (= ρ), allows to match a given tranche s model price with the market price (for a given index CDS level).
12 The implied correlation smile Market Quotes on Aug. 4, 2004 (CDX index spread bp) Tranche 0-3% 3-7% 7-10% 10-15% 15-30% CDX.IG 41.38% 3.49% 1.355% 0.46% 0.14% The market displays an implied correlation smile: Tranche 0-3% 3-7% 7-10% 10-15% 15-30% CDX.IG 21.7% 4.1% 17.8% 18.5% 29.8% The smile shows that the Gaussian copula model is mis-specified (analogous to the implied option smile). Market quotes on June 1st IG4-5Y (CDX index spread of 42 bp): Tranche 0-3% 3-7% 7-10% 10-15% 15-30% CDX.IG 30.5% 0.66%.095%.075% 0.04% The current implied correlation smile: Tranche 0-3% 3-7% 7-10% 10-15% 15-30% CDX.IG 9.08% 5.8% 10.02% 16.77% 27.62%
13 Failure of Copula Model? Events in May 2005 (widening of GM and Ford) had dramatic impact on tranche prices: Equity ([0,3% ]) and index ([0,100%]) widened, while Mezz ([3%,7% ]) tightened! As a result, repricing in correlation markets (equity implied correlation dropped from 20% to 10%). Yet over the same period measures of actual correlation increased: IG4-5Y implied correlation avge pairwise cds correlation /13/ /13/2003 1/13/2004 2/13/2004 3/13/2004 4/13/2004 5/13/2004 6/13/2004 7/13/2004 8/13/2004 9/13/ /13/ /13/ /13/2004 1/13/2005 2/13/2005 3/13/2005 4/13/2005 5/13/2005 6/13/2005 7/13/2005 8/13/2005
14 Looking for better model? May 2005 repricing in correlation markets: impact of cross-sectional dispersion? IG4-5Y implied correlation avge pairwise cds correlation cross-sectional cds dispersion /13/ /13/2003 1/13/2004 2/13/2004 3/13/2004 4/13/2004 5/13/2004 6/13/2004 7/13/2004 8/13/2004 9/13/ /13/ /13/ /13/2004 1/13/2005 2/13/2005 3/13/2005 4/13/2005 5/13/2005 6/13/2005 7/13/2005 8/13/2005 Trading equity implied correlation trading jump to default risk. selling protection on IG4 equity in May 2005 essentially sells protection on first to default basket of autos. Trading senior tranches implied correlation market crash/great depression risk. What is the probability that > 30% of investment grade default in any given year?
15 Reduced-form model with heterogeneous firms Reduced-form approach (Duffie Garleanu (2001), Mortensen (2006)) Assume an intensity process for each underlying name: where M(t) is market wide default intensity. I (t) is industry default component. ɛ i (t) is firm specific component. λ i (t) = ρ i M(t) + β i I (t) + ɛ i (t) Defaults are conditionally independent (doubly stochastic), but there is correlation in default arrival times through M and I. Advantage: conditionally independent defaults (not assumed to arrive jointly). individual hedge ratios can be computed (i.e., impact of widening of GM or Ford). Bespoke can be priced consistently Disadvantage: Cumbersome to implement (lots of parameters and state variables). Difficult to calibrate.
16 Reduced-form model with homogeneous firms This paper proposes simple model of aggregate portfolio losses (assuming homogeneous firms): L t = 1 exp ( γ 1N 1t γ 2N 2t γ 3N 3t) N 1t counts individual firm defaults (γ 1 = 1/125) N 2t counts number of industry wide simultaneous defaults. N 3t counts number of economy wide simultaneous defaults. Each driven by stochastic intensity process: dλ i (t) = σ i p λi (t)dz it Advantage: Simplicity of implementation/computation Disadvantage Assumes joint defaults (to create correlation) Difficult to compute individual name hedge ratios ( analogy to S&P500 index option). Difficult to apply to bespoke portfolios. Technical (minor) issues: Absorption at zero of intensity Intensity unchanged upon default arrival?
17 Approach choose the three intensity processes λ it every day to minimize the cross-sectional fitting error of running spreads on five liquid tranches ([0 3], [3 7], [7 10], [10 15], [15 30]) as well as the index. In addition pick the three volatility parameters σ i and three jump upon default parameters γ i. Allow all parameters to change for every CDX series (i.e., every 6 months). However, note that Difference between IG3-IG4 series is 3 names, IG4-IG5 is 9 names, IG5-IG6 is 4 names
18 Question/Comments Why work with spreads? Need to transform upfront payment on the equity in running spread? (model dependent) Magnitude differences are huge: equity spread 2000bps whereas senior tranche 4 bps. Minimization of sum of squared errors puts too much weight on equity and mezz fitting. RMSE of 5 bps is very good for the equity tranche, but how meaningful for senior tranches? How about fitting implied correlations using implied vols for out of the money options. Time series implications of the model? Since three state variables are fitted every day, clearly can fit three prices perfectly only 2 out of sample points. Parameters of state vector reset every series (despite the fact that at most a few names change at roll). Necessity to bring in time series information. How likely is it to generate these time series through simulation of assumed continuous time process?
19 Question/Comments 2 First Intensity Second Intensity Third Intensity Fig. 3. Intensity Processes. This figure graphs the estimated intensity processes. The vertical division lines denote the roll from one CDX index to the next.
20 Is the CDO tranche market efficient? I don t know! But it seems an ideal candidate not to be: It is a new market (cf. early days of option market or futures market). It is not a transparent market (OTC - still some disagreement on settlement procedures). It is a complicated product (payoff depends on higher order moments of portfolio losses). There is very little data to work with (default data is scarce, but needed to estimate entire joint default distribution). There is no market consensus about the model (post-may consensus is to retain Gaussian Copula model solely as quoting tool). It is affected by technicals, i.e., pipeline of issuances in bespoke CDO and cash CDO markets that trigger hedging demand by broker/dealers. What would be a convincing test of market (in)efficiency? Seems difficult to uncover pure arbitrage (incomplete market/pricing by replication difficult). Need to look at pricing kernel: Are there high sharpe ratio strategies/ good deals? Pre-May 2005 selling protection on equity tranche is negative IR strategy assuming historical default and spread history.
21 Conclusion Very interesting new data on new market. Very elegant simple modeling approach. More to be done on the empirical front: Avoid equally weighting spreads RMSE. Take advantage of time series dimension of model. What is risk-return tradeoff in tranche market? What are hedging possibilities offered by model?
On the relative pricing of long maturity S&P 500 index options and CDX tranches
On the relative pricing of long maturity S&P 5 index options and CDX tranches Pierre Collin-Dufresne Robert Goldstein Fan Yang May 21 Motivation Overview CDX Market The model Results Final Thoughts Securitized
More informationDynamic Models of Portfolio Credit Risk: A Simplified Approach
Dynamic Models of Portfolio Credit Risk: A Simplified Approach John Hull and Alan White Copyright John Hull and Alan White, 2007 1 Portfolio Credit Derivatives Key product is a CDO Protection seller agrees
More informationHedging Default Risks of CDOs in Markovian Contagion Models
Hedging Default Risks of CDOs in Markovian Contagion Models Second Princeton Credit Risk Conference 24 May 28 Jean-Paul LAURENT ISFA Actuarial School, University of Lyon, http://laurent.jeanpaul.free.fr
More informationExhibit 2 The Two Types of Structures of Collateralized Debt Obligations (CDOs)
II. CDO and CDO-related Models 2. CDS and CDO Structure Credit default swaps (CDSs) and collateralized debt obligations (CDOs) provide protection against default in exchange for a fee. A typical contract
More informationDYNAMIC CORRELATION MODELS FOR CREDIT PORTFOLIOS
The 8th Tartu Conference on Multivariate Statistics DYNAMIC CORRELATION MODELS FOR CREDIT PORTFOLIOS ARTUR SEPP Merrill Lynch and University of Tartu artur sepp@ml.com June 26-29, 2007 1 Plan of the Presentation
More informationSYSTEMIC CREDIT RISK: WHAT IS THE MARKET TELLING US? Vineer Bhansali Robert Gingrich Francis A. Longstaff
SYSTEMIC CREDIT RISK: WHAT IS THE MARKET TELLING US? Vineer Bhansali Robert Gingrich Francis A. Longstaff Abstract. The ongoing subprime crisis raises many concerns about the possibility of much broader
More informationCredit Derivatives. By A. V. Vedpuriswar
Credit Derivatives By A. V. Vedpuriswar September 17, 2017 Historical perspective on credit derivatives Traditionally, credit risk has differentiated commercial banks from investment banks. Commercial
More informationSimple Dynamic model for pricing and hedging of heterogeneous CDOs. Andrei Lopatin
Simple Dynamic model for pricing and hedging of heterogeneous CDOs Andrei Lopatin Outline Top down (aggregate loss) vs. bottom up models. Local Intensity (LI) Model. Calibration of the LI model to the
More informationMATH FOR CREDIT. Purdue University, Feb 6 th, SHIKHAR RANJAN Credit Products Group, Morgan Stanley
MATH FOR CREDIT Purdue University, Feb 6 th, 2004 SHIKHAR RANJAN Credit Products Group, Morgan Stanley Outline The space of credit products Key drivers of value Mathematical models Pricing Trading strategies
More informationDelta-Hedging Correlation Risk?
ISFA, Université Lyon 1 International Finance Conference 6 - Tunisia Hammamet, 10-12 March 2011 Introduction, Stéphane Crépey and Yu Hang Kan (2010) Introduction Performance analysis of alternative hedging
More informationOptimal Stochastic Recovery for Base Correlation
Optimal Stochastic Recovery for Base Correlation Salah AMRAOUI - Sebastien HITIER BNP PARIBAS June-2008 Abstract On the back of monoline protection unwind and positive gamma hunting, spreads of the senior
More informationManaging the Newest Derivatives Risks
Managing the Newest Derivatives Risks Michel Crouhy IXIS Corporate and Investment Bank / A subsidiary of NATIXIS Derivatives 2007: New Ideas, New Instruments, New markets NYU Stern School of Business,
More informationAN IMPROVED IMPLIED COPULA MODEL AND ITS APPLICATION TO THE VALUATION OF BESPOKE CDO TRANCHES. John Hull and Alan White
AN IMPROVED IMPLIED COPULA MODEL AND ITS APPLICATION TO THE VALUATION OF BESPOKE CDO TRANCHES John Hull and Alan White Joseph L. Rotman School of Joseph L. Rotman School of Management University of Toronto
More informationBachelier Finance Society, Fifth World Congress London 19 July 2008
Hedging CDOs in in Markovian contagion models Bachelier Finance Society, Fifth World Congress London 19 July 2008 Jean-Paul LAURENT Professor, ISFA Actuarial School, University of Lyon & scientific consultant
More informationAFFI conference June, 24, 2003
Basket default swaps, CDO s and Factor Copulas AFFI conference June, 24, 2003 Jean-Paul Laurent ISFA Actuarial School, University of Lyon Paper «basket defaults swaps, CDO s and Factor Copulas» available
More informationCredit Risk Summit Europe
Fast Analytic Techniques for Pricing Synthetic CDOs Credit Risk Summit Europe 3 October 2004 Jean-Paul Laurent Professor, ISFA Actuarial School, University of Lyon & Scientific Consultant, BNP-Paribas
More informationTHE INFORMATION CONTENT OF CDS INDEX TRANCHES FOR FINANCIAL STABILITY ANALYSIS
B THE INFORMATION CONTENT OF CDS INDEX TRANCHES FOR FINANCIAL STABILITY ANALYSIS Information extracted from credit default swap (CDS) index tranches can provide an important contribution to a forward-looking
More informationNew results for the pricing and hedging of CDOs
New results for the pricing and hedging of CDOs WBS 4th Fixed Income Conference London 20th September 2007 Jean-Paul LAURENT Professor, ISFA Actuarial School, University of Lyon, Scientific consultant,
More informationPricing & Risk Management of Synthetic CDOs
Pricing & Risk Management of Synthetic CDOs Jaffar Hussain* j.hussain@alahli.com September 2006 Abstract The purpose of this paper is to analyze the risks of synthetic CDO structures and their sensitivity
More informationValuation of Forward Starting CDOs
Valuation of Forward Starting CDOs Ken Jackson Wanhe Zhang February 10, 2007 Abstract A forward starting CDO is a single tranche CDO with a specified premium starting at a specified future time. Pricing
More informationDo Leveraged Credit Derivatives Modify Credit Allocation?
Do Leveraged Credit Derivatives Modify Credit Allocation? J.F. Boulier, M. Brière & J.R. Viala Crédit Agricole Asset Management, Université Libre de Bruxelles EDHEC Symposium «Risk and Asset Management»,
More informationNew approaches to the pricing of basket credit derivatives and CDO s
New approaches to the pricing of basket credit derivatives and CDO s Quantitative Finance 2002 Jean-Paul Laurent Professor, ISFA Actuarial School, University of Lyon & Ecole Polytechnique Scientific consultant,
More informationII. What went wrong in risk modeling. IV. Appendix: Need for second generation pricing models for credit derivatives
Risk Models and Model Risk Michel Crouhy NATIXIS Corporate and Investment Bank Federal Reserve Bank of Chicago European Central Bank Eleventh Annual International Banking Conference: : Implications for
More informationPricing Default Events: Surprise, Exogeneity and Contagion
1/31 Pricing Default Events: Surprise, Exogeneity and Contagion C. GOURIEROUX, A. MONFORT, J.-P. RENNE BdF-ACPR-SoFiE conference, July 4, 2014 2/31 Introduction When investors are averse to a given risk,
More informationDynamic Modeling of Portfolio Credit Risk with Common Shocks
Dynamic Modeling of Portfolio Credit Risk with Common Shocks ISFA, Université Lyon AFFI Spring 20 International Meeting Montpellier, 2 May 20 Introduction Tom Bielecki,, Stéphane Crépey and Alexander Herbertsson
More informationOn the Relative Pricing of Long Maturity S&P 500 Index Options and CDX Tranches
On the Relative Pricing of Long Maturity S&P 500 Index Options and CDX Tranches by Pierre Collin-Dufresne Discussion by Markus Leippold Swissquote Conference Ecole Polytechnique Fédérale de Lausanne October,
More informationHOW HAS CDO MARKET PRICING CHANGED DURING THE TURMOIL? EVIDENCE FROM CDS INDEX TRANCHES
C HOW HAS CDO MARKET PRICING CHANGED DURING THE TURMOIL? EVIDENCE FROM CDS INDEX TRANCHES The general repricing of credit risk which started in summer 7 has highlighted signifi cant problems in the valuation
More informationAnalytical Pricing of CDOs in a Multi-factor Setting. Setting by a Moment Matching Approach
Analytical Pricing of CDOs in a Multi-factor Setting by a Moment Matching Approach Antonio Castagna 1 Fabio Mercurio 2 Paola Mosconi 3 1 Iason Ltd. 2 Bloomberg LP. 3 Banca IMI CONSOB-Università Bocconi,
More informationMBAX Credit Default Swaps (CDS)
MBAX-6270 Credit Default Swaps Credit Default Swaps (CDS) CDS is a form of insurance against a firm defaulting on the bonds they issued CDS are used also as a way to express a bearish view on a company
More informationTHE ROLE OF DEFAULT CORRELATION IN VALUING CREDIT DEPENDANT SECURITIES
THE ROLE OF DEFAULT CORRELATION IN VALUING CREDIT DEPENDANT SECURITIES by William Matthew Nestor Bobey A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate
More informationFinancial Risk Management
Financial Risk Management Professor: Thierry Roncalli Evry University Assistant: Enareta Kurtbegu Evry University Tutorial exercices #3 1 Maximum likelihood of the exponential distribution 1. We assume
More informationThe Liquidity of Credit Default Index Swap Networks. Richard Haynes and Lihong McPhail U.S. Commodity Futures Trading Commission
The Liquidity of Credit Default Index Swap Networks Richard Haynes and Lihong McPhail U.S. Commodity Futures Trading Commission 1 Motivation Single name Credit Default Swaps (CDS) are used to buy and sell
More informationTrading motivated by anticipated changes in the expected correlations of credit defaults and spread movements among specific credits and indices.
Arbitrage Asset-backed security (ABS) Asset/liability management (ALM) Assets under management (AUM) Back office Bankruptcy remoteness Brady bonds CDO capital structure Carry trade Collateralized debt
More informationAdvanced Tools for Risk Management and Asset Pricing
MSc. Finance/CLEFIN 2014/2015 Edition Advanced Tools for Risk Management and Asset Pricing June 2015 Exam for Non-Attending Students Solutions Time Allowed: 120 minutes Family Name (Surname) First Name
More information1.2 Product nature of credit derivatives
1.2 Product nature of credit derivatives Payoff depends on the occurrence of a credit event: default: any non-compliance with the exact specification of a contract price or yield change of a bond credit
More informationA Generic One-Factor Lévy Model for Pricing Synthetic CDOs
A Generic One-Factor Lévy Model for Pricing Synthetic CDOs Wim Schoutens - joint work with Hansjörg Albrecher and Sophie Ladoucette Maryland 30th of September 2006 www.schoutens.be Abstract The one-factor
More informationIntroduction to credit risk
Introduction to credit risk Marco Marchioro www.marchioro.org December 1 st, 2012 Introduction to credit derivatives 1 Lecture Summary Credit risk and z-spreads Risky yield curves Riskless yield curve
More informationTheoretical Problems in Credit Portfolio Modeling 2
Theoretical Problems in Credit Portfolio Modeling 2 David X. Li Shanghai Advanced Institute of Finance (SAIF) Shanghai Jiaotong University(SJTU) November 3, 2017 Presented at the University of South California
More informationCREDIT RATINGS. Rating Agencies: Moody s and S&P Creditworthiness of corporate bonds
CREDIT RISK CREDIT RATINGS Rating Agencies: Moody s and S&P Creditworthiness of corporate bonds In the S&P rating system, AAA is the best rating. After that comes AA, A, BBB, BB, B, and CCC The corresponding
More informationEXAMINATION II: Fixed Income Analysis and Valuation. Derivatives Analysis and Valuation. Portfolio Management. Questions.
EXAMINATION II: Fixed Income Analysis and Valuation Derivatives Analysis and Valuation Portfolio Management Questions Final Examination March 2010 Question 1: Fixed Income Analysis and Valuation (56 points)
More informationValuation of a CDO and an n th to Default CDS Without Monte Carlo Simulation
Forthcoming: Journal of Derivatives Valuation of a CDO and an n th to Default CDS Without Monte Carlo Simulation John Hull and Alan White 1 Joseph L. Rotman School of Management University of Toronto First
More informationRisk Management aspects of CDOs
Risk Management aspects of CDOs CDOs after the crisis: Valuation and risk management reviewed 30 September 2008 Jean-Paul LAURENT ISFA Actuarial School, University of Lyon & BNP Paribas http://www.jplaurent.info
More informationCDO Market Overview & Outlook. CDOs in the Heartland. Lang Gibson Director of Structured Credit Research March 25, 2004
CDO Market Overview & Outlook CDOs in the Heartland Lang Gibson Director of Structured Credit Research March 25, 24 23 featured record volumes despite diminishing arbitrage Global CDO Growth: 1995-23 $
More informationCredit Risk Models with Filtered Market Information
Credit Risk Models with Filtered Market Information Rüdiger Frey Universität Leipzig Bressanone, July 2007 ruediger.frey@math.uni-leipzig.de www.math.uni-leipzig.de/~frey joint with Abdel Gabih and Thorsten
More information3.4 Copula approach for modeling default dependency. Two aspects of modeling the default times of several obligors
3.4 Copula approach for modeling default dependency Two aspects of modeling the default times of several obligors 1. Default dynamics of a single obligor. 2. Model the dependence structure of defaults
More informationCOPYRIGHTED MATERIAL. 1 The Credit Derivatives Market 1.1 INTRODUCTION
1 The Credit Derivatives Market 1.1 INTRODUCTION Without a doubt, credit derivatives have revolutionised the trading and management of credit risk. They have made it easier for banks, who have historically
More informationDynamic Factor Copula Model
Dynamic Factor Copula Model Ken Jackson Alex Kreinin Wanhe Zhang March 7, 2010 Abstract The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback
More informationApplications of CDO Modeling Techniques in Credit Portfolio Management
Applications of CDO Modeling Techniques in Credit Portfolio Management Christian Bluhm Credit Portfolio Management (CKR) Credit Suisse, Zurich Date: October 12, 2006 Slide Agenda* Credit portfolio management
More informationImplied Correlations: Smiles or Smirks?
Implied Correlations: Smiles or Smirks? Şenay Ağca George Washington University Deepak Agrawal Diversified Credit Investments Saiyid Islam Standard & Poor s. June 23, 2008 Abstract We investigate whether
More informationComparison results for credit risk portfolios
Université Claude Bernard Lyon 1, ISFA AFFI Paris Finance International Meeting - 20 December 2007 Joint work with Jean-Paul LAURENT Introduction Presentation devoted to risk analysis of credit portfolios
More informationPoint De Vue: Operational challenges faced by asset managers to price OTC derivatives Laurent Thuilier, SGSS. Avec le soutien de
Point De Vue: Operational challenges faced by asset managers to price OTC derivatives 2012 01 Laurent Thuilier, SGSS Avec le soutien de JJ Mois Année Operational challenges faced by asset managers to price
More informationSemi-Analytical Valuation of Basket Credit Derivatives in Intensity-Based Models
Semi-Analytical Valuation of Basket Credit Derivatives in Intensity-Based Models Allan Mortensen This version: January 31, 2005 Abstract This paper presents a semi-analytical valuation method for basket
More informationCorrelated Default Modeling with a Forest of Binomial Trees
Correlated Default Modeling with a Forest of Binomial Trees Santhosh Bandreddi Merrill Lynch New York, NY 10080 santhosh bandreddi@ml.com Rong Fan Gifford Fong Associates Lafayette, CA 94549 rfan@gfong.com
More informationCredit Risk in Banking
Credit Risk in Banking CREDIT DERIVATIVES Hull J., Options, futures, and other derivatives, Ed. 7, chapter 23 Sebastiano Vitali, 2017/2018 Credit derivatives Credit derivatives are contracts where the
More informationComparison of market models for measuring and hedging synthetic CDO tranche spread risks
Eur. Actuar. J. (2011) 1 (Suppl 2):S261 S281 DOI 10.1007/s13385-011-0025-1 ORIGINAL RESEARCH PAPER Comparison of market models for measuring and hedging synthetic CDO tranche spread risks Jack Jie Ding
More informationPricing Simple Credit Derivatives
Pricing Simple Credit Derivatives Marco Marchioro www.statpro.com Version 1.4 March 2009 Abstract This paper gives an introduction to the pricing of credit derivatives. Default probability is defined and
More informationInstitute of Actuaries of India. Subject. ST6 Finance and Investment B. For 2018 Examinationspecialist Technical B. Syllabus
Institute of Actuaries of India Subject ST6 Finance and Investment B For 2018 Examinationspecialist Technical B Syllabus Aim The aim of the second finance and investment technical subject is to instil
More informationCB Asset Swaps and CB Options: Structure and Pricing
CB Asset Swaps and CB Options: Structure and Pricing S. L. Chung, S.W. Lai, S.Y. Lin, G. Shyy a Department of Finance National Central University Chung-Li, Taiwan 320 Version: March 17, 2002 Key words:
More informationBilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps
Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps Agostino Capponi California Institute of Technology Division of Engineering and Applied Sciences
More informationAdvances in Valuation Adjustments. Topquants Autumn 2015
Advances in Valuation Adjustments Topquants Autumn 2015 Quantitative Advisory Services EY QAS team Modelling methodology design and model build Methodology and model validation Methodology and model optimisation
More informationANALYTICAL FINANCE II Floating Rate Notes, fixed coupon bonds and swaps
ANALYTICAL FINANCE II Floating Rate Notes, fixed coupon bonds and swaps Ali Salih & Vadim Suvorin Division of Applied Mathematics Mälardalen University, Box 883, 72132 Västerȧs, SWEDEN December 15, 2010
More informationRapid computation of prices and deltas of nth to default swaps in the Li Model
Rapid computation of prices and deltas of nth to default swaps in the Li Model Mark Joshi, Dherminder Kainth QUARC RBS Group Risk Management Summary Basic description of an nth to default swap Introduction
More informationOn the Relative Pricing of long Maturity. S&P 500 Index Options and CDX Tranches 1
On the Relative Pricing of long Maturity S&P 500 Index Options and CDX Tranches 1 Pierre Collin-Dufresne 2 Robert S. Goldstein 3 Fan Yang 4 First Version: October 2008 This Version: January 25, 2010 1
More informationAn Empirical Analysis of the Pricing of Collateralized Debt Obligations
THE JOURNAL OF FINANCE VOL. LXIII, NO. 2 APRIL 2008 An Empirical Analysis of the Pricing of Collateralized Debt Obligations FRANCIS A. LONGSTAFF and ARVIND RAJAN ABSTRACT We use the information in collateralized
More informationWANTED: Mathematical Models for Financial Weapons of Mass Destruction
WANTED: Mathematical for Financial Weapons of Mass Destruction. Wim Schoutens - K.U.Leuven - wim@schoutens.be Wim Schoutens, 23-10-2008 Eindhoven, The Netherlands - p. 1/23 Contents Contents This talks
More informationChapter 2. Credit Derivatives: Overview and Hedge-Based Pricing. Credit Derivatives: Overview and Hedge-Based Pricing Chapter 2
Chapter 2 Credit Derivatives: Overview and Hedge-Based Pricing Chapter 2 Derivatives used to transfer, manage or hedge credit risk (as opposed to market risk). Payoff is triggered by a credit event wrt
More informationContagion models with interacting default intensity processes
Contagion models with interacting default intensity processes Yue Kuen KWOK Hong Kong University of Science and Technology This is a joint work with Kwai Sun Leung. 1 Empirical facts Default of one firm
More informationBy Khader Shaik CDS Market - The Big Picture Copyright 2011 Khader Shaik (ksvali.com) 1
By Khader Shaik 1 CDS Credit Default Swap CDS is an agreement between two parties in reference to an external entity known as Reference Entity, in which one party known as Protection Buyer pays the periodic
More information25 Oct 2010 QIAO Yang SHEN Si
Credit Derivatives: CDS, CDO and financial crisis 25 Oct 2010 QIAO Yang SHEN Si 1 Agenda Historical background: what is Credit Default Swaps (CDS) and Collateralized Default Obligation (CDO) Issue and
More informationImplied Correlations: Smiles or Smirks?
Implied Correlations: Smiles or Smirks? Şenay Ağca George Washington University Deepak Agrawal Diversified Credit Investments Saiyid Islam Standard & Poor s This version: Aug 15, 2007. Abstract With standardized
More informationCounterparty Risk Modeling for Credit Default Swaps
Counterparty Risk Modeling for Credit Default Swaps Abhay Subramanian, Avinayan Senthi Velayutham, and Vibhav Bukkapatanam Abstract Standard Credit Default Swap (CDS pricing methods assume that the buyer
More informationQua de causa copulae me placent?
Barbara Choroś Wolfgang Härdle Institut für Statistik and Ökonometrie CASE - Center for Applied Statistics and Economics Humboldt-Universität zu Berlin Motivation - Dependence Matters! The normal world
More informationPrice Calibration and Hedging of Correlation Dependent Credit Derivatives using a Structural Model with α-stable Distributions
Universität Karlsruhe (TH) Institute for Statistics and Mathematical Economic Theory Chair of Statistics, Econometrics and Mathematical Finance Prof. Dr. S.T. Rachev Price Calibration and Hedging of Correlation
More informationCredit Ratings and Securitization
Credit Ratings and Securitization Bachelier Congress June 2010 John Hull 1 Agenda To examine the derivatives that were created from subprime mortgages To determine whether the criteria used by rating agencies
More informationDo rare events explain CDX tranche spreads?
Do rare events explain CDX tranche spreads? Sang Byung Seo University of Houston Jessica A. Wachter University of Pennsylvania December 31, 215 and NBER Abstract We investigate whether a model with a time-varying
More informationAn Approximation for Credit Portfolio Losses
An Approximation for Credit Portfolio Losses Rüdiger Frey Universität Leipzig Monika Popp Universität Leipzig April 26, 2007 Stefan Weber Cornell University Introduction Mixture models play an important
More informationApplying hedging techniques to credit derivatives
Applying hedging techniques to credit derivatives Risk Training Pricing and Hedging Credit Derivatives London 26 & 27 April 2001 Jean-Paul LAURENT Professor, ISFA Actuarial School, University of Lyon,
More informationCredit Risk Management: A Primer. By A. V. Vedpuriswar
Credit Risk Management: A Primer By A. V. Vedpuriswar February, 2019 Altman s Z Score Altman s Z score is a good example of a credit scoring tool based on data available in financial statements. It is
More informationTopQuants. Integration of Credit Risk and Interest Rate Risk in the Banking Book
TopQuants Integration of Credit Risk and Interest Rate Risk in the Banking Book 1 Table of Contents 1. Introduction 2. Proposed Case 3. Quantifying Our Case 4. Aggregated Approach 5. Integrated Approach
More informationSynthetic CDO Pricing Using the Student t Factor Model with Random Recovery
Synthetic CDO Pricing Using the Student t Factor Model with Random Recovery UNSW Actuarial Studies Research Symposium 2006 University of New South Wales Tom Hoedemakers Yuri Goegebeur Jurgen Tistaert Tom
More informationFactor Copulas: Totally External Defaults
Martijn van der Voort April 8, 2005 Working Paper Abstract In this paper we address a fundamental problem of the standard one factor Gaussian Copula model. Within this standard framework a default event
More informationApproximating Correlated Defaults
Department of Finance University of Illinois at Chicago 27 September 2012 National Bank of Slovakia Introduction In the 2008 2009 financial crisis: US households alone lost $11 Tn in wealth; and, Structured
More informationHedging Basket Credit Derivatives with CDS
Hedging Basket Credit Derivatives with CDS Wolfgang M. Schmidt HfB - Business School of Finance & Management Center of Practical Quantitative Finance schmidt@hfb.de Frankfurt MathFinance Workshop, April
More informationCREDIT DEFAULT SWAPS AND THEIR APPLICATION
CREDIT DEFAULT SWAPS AND THEIR APPLICATION Dr Ewelina Sokołowska, Dr Justyna Łapińska Nicolaus Copernicus University Torun, Faculty of Economic Sciences and Management, ul. Gagarina 11, 87-100 Toruń, e-mail:
More informationVasicek Model Copulas CDO and CSO Other products. Credit Risk. Lecture 4 Portfolio models and Asset Backed Securities (ABS) Loïc BRIN
Credit Risk Lecture 4 Portfolio models and Asset Backed Securities (ABS) École Nationale des Ponts et Chaussées Département Ingénieurie Mathématique et Informatique (IMI) Master II Credit Risk - Lecture
More informationFinal Thesis. CDS Model and Market Spreads Amid the Financial Crisis. Dominik Jaretzke, Maastricht University
Final Thesis CDS Model and Market Spreads Amid the Financial Crisis Dominik Jaretzke, Maastricht University Final Thesis CDS Model and Market Spreads Amid the Financial Crisis 1 Dominik Jaretzke, Maastricht
More informationPricing Convertible Bonds under the First-Passage Credit Risk Model
Pricing Convertible Bonds under the First-Passage Credit Risk Model Prof. Tian-Shyr Dai Department of Information Management and Finance National Chiao Tung University Joint work with Prof. Chuan-Ju Wang
More informationEXAMINATION II: Fixed Income Valuation and Analysis. Derivatives Valuation and Analysis. Portfolio Management
EXAMINATION II: Fixed Income Valuation and Analysis Derivatives Valuation and Analysis Portfolio Management Questions Final Examination March 2011 Question 1: Fixed Income Valuation and Analysis (43 points)
More informationValuing Credit Derivatives Using an Implied Copula Approach. John Hull and Alan White* Joseph L. Rotman School of Management
Journal of Derivatives, Fall 2006 Valuing Credit Derivatives Using an Implied Copula Approach John Hull and Alan White* Joseph L. Rotman School of Management First Draft: June 2005 This Draft: November
More informationCREDIT RISK DEPENDENCE MODELING FOR COLLATERALIZED DEBT OBLIGATIONS
Gabriel GAIDUCHEVICI The Bucharest University of Economic Studies E-mail: gaiduchevici@gmail.com Professor Bogdan NEGREA The Bucharest University of Economic Studies E-mail: bogdan.negrea@fin.ase.ro CREDIT
More informationRating of European sovereign bonds and its impact on credit default swaps (CDS) and government bond yield spreads
Rating of European sovereign bonds and its impact on credit default swaps (CDS) and government bond yield spreads Supervised by: Prof. Günther Pöll Diploma Presentation Plass Stefan B.A. 21 th October
More informationDerivatives: part I 1
Derivatives: part I 1 Derivatives Derivatives are financial products whose value depends on the value of underlying variables. The main use of derivatives is to reduce risk for one party. Thediverse range
More informationCounterparty Risk and CVA
Counterparty Risk and CVA Stephen M Schaefer London Business School Credit Risk Elective Summer 2012 Net revenue included a $1.9 billion gain from debit valuation adjustments ( DVA ) on certain structured
More informationAdvanced Quantitative Methods for Asset Pricing and Structuring
MSc. Finance/CLEFIN 2017/2018 Edition Advanced Quantitative Methods for Asset Pricing and Structuring May 2017 Exam for Non Attending Students Time Allowed: 95 minutes Family Name (Surname) First Name
More informationVALUE-ADDING ACTIVE CREDIT PORTFOLIO MANAGEMENT
VALUE-ADDING ACTIVE CREDIT PORTFOLIO MANAGEMENT OPTIMISATION AT ALL LEVELS Dr. Christian Bluhm Head Credit Portfolio Management Credit Suisse, Zurich September 28-29, 2005, Wiesbaden AGENDA INTRODUCTION
More informationManaging the Newest Derivatives Risks
Managing the Newest Derivatives Risks Michel Crouhy NATIXIS Corporate and Investment Bank European Summer School in Financial Mathematics Tuesday, September 9, 2008 Natixis 2006 Agenda Some Practical Aspects
More informationCredit Derivatives An Overview and the Basics of Pricing
Master Programme in Advanced Finance Master Thesis, CFF2005:01 Centre for Finance Credit Derivatives An Overview and the Basics of Pricing Master Thesis Authors: Karin Kärrlind, 760607-4925 Jakob Tancred,
More informationPricing Synthetic CDO Tranche on ABS
Pricing Synthetic CDO Tranche on ABS Yan Li A thesis submitted for the degree of Doctor of Philosophy of the University of London Centre for Quantitative Finance Imperial College London September 2007
More informationDynamic Wrong-Way Risk in CVA Pricing
Dynamic Wrong-Way Risk in CVA Pricing Yeying Gu Current revision: Jan 15, 2017. Abstract Wrong-way risk is a fundamental component of derivative valuation that was largely neglected prior to the 2008 financial
More informationGRANULARITY ADJUSTMENT FOR DYNAMIC MULTIPLE FACTOR MODELS : SYSTEMATIC VS UNSYSTEMATIC RISKS
GRANULARITY ADJUSTMENT FOR DYNAMIC MULTIPLE FACTOR MODELS : SYSTEMATIC VS UNSYSTEMATIC RISKS Patrick GAGLIARDINI and Christian GOURIÉROUX INTRODUCTION Risk measures such as Value-at-Risk (VaR) Expected
More information